Question about remortgaging?

I took out a 5 year fixed mortgage for my first house purchase and I still have just under 4 years to go but wanted to get clear in my mind about how a remortgage works when my fixed deal ends.

So in the time remaining I am hoping to save up around 40k. So what I wanted to do is get another mortgage and put this 40k towards it. Is this possible, what costs are involved, can i go onto another fixed deal?

Just wanting to get things all stright in my mind is all.

Thanks.